Applied Time Series Analysis II. Proceedings of the Second by David F. Findley

By David F. Findley

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Extra resources for Applied Time Series Analysis II. Proceedings of the Second Applied Time Series Symposium Held in Tulsa, Oklahoma, March 3–5, 1980

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We would do well, then, to consider algorithms which are as cost effective as possible. Here, then, is a challenge. recursive filter equation y(B) =§ff}u

0 0 A9 1 0 . . 0 » i t i t 1 1 i i 0 . . A2 X + in 1 0 ... 0 i 0 ! i 1 i 0 A 0 i 1 f 0 . . i i i 0 i 1 y = [ekj]x Both realizations may be shown to be minimal, and each has its own advantages and disadvantages. Let us now consider the case of a true multivariable system and pose the problem of finding a minimal realization again. A glance at the Jordan Canonical Form above will tell us not to waste much time looking for an easy extension there, because we factored polynomials to arrive at it.

How do we obtain a minimal realization of a multivariable input-output system? Again, we may turn our attention to state variable methods and hope that therein lies an answer. Again, how­ ever, a new field is being born and the search for a suitable answer to this question continues. A number of investigators have considered the problem of finding suitable multidimensional extensions of the state dynamic equations and of the concepts of controllability, Higher Dimensional Signal Processing 45 observability, and minimality.

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